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Question Number 168341 by Tibo last updated on 08/Apr/22

$$\int {(1+x^2)}^{3}dx=?$$

Answered by Florian last updated on 08/Apr/22

$$=\int 1+3x^2+3x^4+x^{6}dx$$$$=\int 1dx+\int 3x^{2}dx+\int 3x^{4}dx+\int x^{6}dx$$$$\int 1dx=x\to \int 3x^2=x^3\to \int 3x^{4}dx=\frac{3x^5}{5}\to \int x^{6}dx=\frac{x^7}{7}$$$$$$

Commented by Florian last updated on 08/Apr/22

$$=x+x^3+\frac{3x^5}{5}+\frac{x^7}{7}$$

Commented by Tibo last updated on 08/Apr/22

$$thankyou!$$

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